But music is not playing via Bluetooth, & is using the mobile speaker in Nokia Lumia 720, why ?

The point here is, I am not able to listen via Bluetooth not only in Nokia Music, But also in any Music Applications that are available in Market Store.
Inability to listen to music via Bluetooth, is extended to You-tube videos, or for that matter any Videos in Nokia Lumia 720.
I suggest, if you could help me with any application, similar to BTMONO in Android OS, that allows/enables to listen music via Bluetooth, specifically MONO BLUETOOTH.

My point is, if this same Samsung Mono Bluetooth model HM1100 can work on all Android OS phones, using a third party application called BTMONO ( by BEDOIG), then MICROSOFT / NOKIA should also try to develop similar application to support music / videos using MONO Bluetooth.

In ANDROID OS, not only BTMONO, there are loads and tons of third party applications now, that supports streaming music for MONO Bluetooth without A2DP profile.
ANDROID Phones are great, when compared to Windows Phone.

If that is not possible, please suggest me a good Bluetooth model that is of same size as of Samsung HM1100, with NO WIRES, & able to listen to music in one ear. If you answer this, then I would consider that only part of my problem is resolved for my Nokia Lumia 720.

But music is not playing via Bluetooth, & is using the mobile speaker in Nokia Lumia 720, why ?

The point here is, I am not able to listen via Bluetooth not only in Nokia Music, But also in any Music Applications that are available in Market Store.
Inability to listen to music via Bluetooth, is extended to You-tube videos, or for that matter any Videos in Nokia Lumia 720.
I suggest, if you could help me with any application, similar to BTMONO in Android OS, that allows/enables to listen music via Bluetooth, specifically MONO BLUETOOTH.

You seem to of failed at reading what i said, so i will elaborate so its easier to understand. Audio for Calls (no matter skype, line, cellular, etc) is transmitted over the Bluetooth Hands Free profile. HOWEVER, music and general/gaming application audio is transmitted via a separate audio profile. Now all BT headsets support handsfree profile. Thats what they are built for, but not all support the audio profile which music is streamed over. Also, it does not matter whether they are stereo or mono. I had a headset which was mono but played my music fine.

The reason android can do that though is because android is a very open and fluid os, as well as there is a key fact: there is more than one bt audio profile that supports music. i cannot remember the names of them, but let me put it this way: Some headsets opt to use the lesser implemented profile, so in said scenarios, devices that do not support said profile but support the commonly used profile will appear to have no support at all when paired with that headset.

there are a multitude of headsets out there that support music playback, you just have to check the packaging to make sure. Furthermore, some headsets are programmed with an OS in mind, meaning other OSes will have a harder time due to optimizations made on the headset for that specific os.

And I have almost the opposite problem. My Plantronics Voyager Pro+ plays music and the audio is fine.
Problem is when the bluetooth is paired, the ONLY way to hear the phone ring, hear notifications etc. is thru the earpiece!
This earpiece is smart and knows when it's on the ear or not. With Android, if I had the earpiece off my ear, sounds and notifications would go to the speaker on the phone.
For some reason WP wants to keep the connection always on. And there is no control whatsoever on how to manipulate this.

Play music through Hands free BT headset has always been a hack. A2DP profile exists for a reason. There are plenty of BT headsets out there that support both profiles and also mono. Why would insists on have the OS to support the hack as an advantage? A $10 BT mono headset that can handle both profiles isn't too much to go with the proper/standard ways of playing music.